The method is called cover crops or compost covered vegetable garden -a layer of straws and leaves and compost keeps the soil constantly moist, and prevents weeds to grow up.
As the straw and hay mulches fresch and fertile soil is added to the vegetable garden.
Here are pictures of my garden where I use this technique with cover crops. There is some work to embed the compost and grass around the plants but once you're done it all looks nice and cozy. Plus, you almost never have to clear except for just a few small weeds coming up.

cover crops vegetables are less sensitive
It is good if the cover material has first been in a bag and compacted or if it is a bit wet and heavy.
One must add a rather thick layer, perhaps 7-10 cm thick should be fine? But the thicker the layer, the less likely that weeds will appear. It is good to use materials that have been laying outside and started the mulching process a bit. Use grass clippings that is already a bit wet and heavy instead of crisp, dry, airy and fluffy grass. Compost leaves is also good, you can mix it with grass clippings or hay.
The risk of pests decreases with cover crops plus the crops are less sensitive to temperature changes. The soil gets fertile, moist and fluffy.

Cover crops saves water
You almost never have to water, the layer keeps the ground moist